Abstract

Recently, the existence of a perfect lens has been predicted, made of an artificial material that has a negative electric permittivity and a negative magnetic permeability. For optical frequencies a poormans version is predicted to exist in the sub-wavelength limit. Then, only the permittivity has to be negative, a demand that metals fulfill at optical frequencies. We propose a new measurement scheme to verify the performance of such a negative permittivity near-perfect lens at optical frequencies. The scheme is based on near-field scanning optical microscopy and single molecule detection. Prerequisite near-field single molecule data, necessary to assess the performance of the lens, is presented. A numerical evaluation, which includes absorption, of the expected performance of a slab of a realistic negative permittivity material confirms the merits of the scheme.

© 2005 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. V. G. Veselago, �??The electrodynamics of substances with simultaneously negative values of epsilon and µ,�?? Sov. Phys. Usp. 10, 509�??514 (1968).
    [CrossRef]
  3. R. A. Shelby, D. R. Smith, and S. Schultz, �??Experimental verification of a negative index of refraction,�?? Science 292, 77�??79 (2001).
    [CrossRef] [PubMed]
  4. X. S. Rao and C. K. Ong, �??Subwavelength imaging by a left-handed material superlens,�?? Phys. Rev. E 68, 067601 (2003).
    [CrossRef]
  5. X. S. Rao and C. K. Ong, �??Amplification of evanescent waves in a lossy left-handed material slab,�?? Phys. Rev. B 68, 113103 (2003).
    [CrossRef]
  6. N. C. Panoiu and R. M. Osgood, �??Numerical investigation of negative refractive index metamaterials at infrared and optical frequencies,�?? Opt. Commun. 223, 331�??337 (2003).
    [CrossRef]
  7. P. G. Kik, S. A. Maier, and H. A. Atwater, �??Image resolution of surface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources,�?? Phys. Rev. B 69, 045418 (2004).
    [CrossRef]
  8. D. O. S. Melville, R. J. Blaikie, and C. R.Wolf, �??Submicron imaging with a planar silver lens,�?? Appl. Phys. Lett. 84, 4403�??4405 (2004).
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    [CrossRef]
  11. M. L.M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, �??Photon scanning tunneling optical microscopy with a three-dimensional multiheight imaging mode,�?? Appl. Phys. Lett. 77, 4092�??4094 (2000).
    [CrossRef]
  12. J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, and N. F. V. Hulst, �??Single molecule mapping of the optical field distribution of probes for near-field microscopy,�?? J. Microscopy-Oxford 194, 477�??482 (1999).
    [CrossRef]
  13. N. F. van Hulst, J. A. Veerman, M. F. Garcia-Parajo, and L. Kuipers, �??Analysis of individual (macro)molecules and proteins using near-field optics,�?? J. Chem. Phys. 112, 7799�??7810 (2000).
    [CrossRef]
  14. B. Sick, B. Hecht, U. P. Wild, and L. Novotny, �??Probing confined fields with single molecules and vice versa,�?? J. Microscopy-Oxford 202, 365�??373 (2001).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]

Appl. Phys. Lett. (3)

D. O. S. Melville, R. J. Blaikie, and C. R.Wolf, �??Submicron imaging with a planar silver lens,�?? Appl. Phys. Lett. 84, 4403�??4405 (2004).
[CrossRef]

J. A. Veerman, A.M. Otter, L. Kuipers, and N. F. van Hulst, �??High definition aperture probes for near-field optical microscopy fabricated by focused ion beam milling,�?? Appl. Phys. Lett. 72, 3115�??3117 (1998).
[CrossRef]

M. L.M. Balistreri, J. P. Korterik, L. Kuipers, and N. F. van Hulst, �??Photon scanning tunneling optical microscopy with a three-dimensional multiheight imaging mode,�?? Appl. Phys. Lett. 77, 4092�??4094 (2000).
[CrossRef]

J. Chem. Phys. (1)

N. F. van Hulst, J. A. Veerman, M. F. Garcia-Parajo, and L. Kuipers, �??Analysis of individual (macro)molecules and proteins using near-field optics,�?? J. Chem. Phys. 112, 7799�??7810 (2000).
[CrossRef]

J. Microscopy-Oxford (3)

B. Sick, B. Hecht, U. P. Wild, and L. Novotny, �??Probing confined fields with single molecules and vice versa,�?? J. Microscopy-Oxford 202, 365�??373 (2001).
[CrossRef]

O. J. F. Martin and M. Paulus, �??Influence of metal roughness on the near-field generated by an aperture/apertureless probe,�?? J. Microscopy-Oxford 205, 147�??152 (2002).
[CrossRef]

J. A. Veerman, M. F. Garcia-Parajo, L. Kuipers, and N. F. V. Hulst, �??Single molecule mapping of the optical field distribution of probes for near-field microscopy,�?? J. Microscopy-Oxford 194, 477�??482 (1999).
[CrossRef]

J. Modern Opt. (1)

S. A. Ramakrishna and J. B. Pendry, �??The asymmetric lossy near-perfect lens,�?? J. Modern Opt. 49, 1747�??1762 (2002).
[CrossRef]

Opt. Commun. (1)

N. C. Panoiu and R. M. Osgood, �??Numerical investigation of negative refractive index metamaterials at infrared and optical frequencies,�?? Opt. Commun. 223, 331�??337 (2003).
[CrossRef]

Opt. Express (1)

Philips Res. Rep. (1)

C. J. Bouwkamp, �??On Bethe�??s theory of diffraction by small holes,�?? Philips Res. Rep. 5, 321�??332 (1950).

Phys. Rev. (1)

H. Bethe, �??Theory of Diffraction by Small Holes,�?? Phys. Rev. 66, 163 (1944).
[CrossRef]

Phys. Rev. B (2)

P. G. Kik, S. A. Maier, and H. A. Atwater, �??Image resolution of surface-plasmon-mediated near-field focusing with planar metal films in three dimensions using finite-linewidth dipole sources,�?? Phys. Rev. B 69, 045418 (2004).
[CrossRef]

X. S. Rao and C. K. Ong, �??Amplification of evanescent waves in a lossy left-handed material slab,�?? Phys. Rev. B 68, 113103 (2003).
[CrossRef]

Phys. Rev. E (1)

X. S. Rao and C. K. Ong, �??Subwavelength imaging by a left-handed material superlens,�?? Phys. Rev. E 68, 067601 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

1. J. B. Pendry, �??Negative refraction makes a perfect lens,�?? Phys. Rev. Lett. 85, 3966�??3969 (2000).
[CrossRef] [PubMed]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, �??Experimental verification of a negative index of refraction,�?? Science 292, 77�??79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, �??The electrodynamics of substances with simultaneously negative values of epsilon and µ,�?? Sov. Phys. Usp. 10, 509�??514 (1968).
[CrossRef]

Other (2)

Computer Simulation Technology, URL http://www.cst.com.

D. E. Gray, ed., American Institute of Physics Handbook, 3rd ed. (McGraw-Hill Book Company, 1972).

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Figures (8)

Fig. 1.
Fig. 1.

Proposed near field set-up to evaluate the performance of the NPM lens. A NSOM probe is used as a sub-wavelength source of evanescent fields and is brought to within a few tens of nanometers away from the NPM lens by using shear-force feedback. The NPM lens is placed on a layer of a polymer matrix containing fluorescent molecules that are individually addressable and will act as sub-wavelength detectors sensitive to the vectorial nature of the local electromagnetic field. Shown in the red circle is a FIB image of a real NSOM probe with an aperture diameter of ~100 nm.

Fig. 2.
Fig. 2.

False color representation of a Bethe-Bouwkamp calculation of the fields present at the end face of a near-field scanning probe with linearly polarized excitation light. Shown from left to right are the absolute values of Ex, Ey and Ez respectively. The field amplitudes are normalized to the maximum field amplitude of Ex . Aperture diameter =100 nm, indicated by the white circle. Distance to the aperture =20 nm and the wavelength =514 nm. The rich variety of the field at the end face of the NSOM probe is evident.

Fig. 3.
Fig. 3.

(a) Mapping of the field components of a NSOM probe by a molecule with a dipole moment as indicated by θ and ϕ, using circular polarization. The Ex and Ey fields of the fluorescence light are color coded as red and green respectively. Because of the circular polarization of the exciting field, the Ez field is mapped as a donut-like shape. (b) Single molecule data obtained with NSOM using circularly polarized excitation light of 514 nm. The aperture diameter of the NSOM probe used in the measurement is 130 nm. The in-plane polarization of the emitted light is color-coded as in (a). A typical result for the three orthogonal directions are indicated by arrows. The red and green arrows point to molecules that have probed the Ex and Ey fields, respectively. A typical result for the Ez field is indicated by the yellow arrow. The Ez field is probed by an out-of-plane oriented (θ=0) molecule and the typical donut shape is retrieved. Clearly, the single molecule is capable of detecting the vectorial nature of the local electromagnetic field.

Fig. 4.
Fig. 4.

Schematic layout of the simulation space (side view). A planar wave impinges a perfectly electrically conducting sheet, with a 100 nm circular aperture cut from it. The sheet with the aperture is our model for the NSOM probe, corresponding to a Bethe-Bouwkamp configuration. The Ez and Ex fields are evaluated at locations 1 and 2, both with and without a negative permittivity material slab. The results of these simulations are presented in Fig. 5.

Fig. 5.
Fig. 5.

Simulation results. Shown are the components |Ex | and |Ez | in Fig. (a) and (b) respectively. The normalized magnitude of the field components is plotted, evaluated at position 1 (green curve) and at position 2 (blue curve) as displayed in Fig. 4, both for the slab-less situation. Clearly visible is the broadening of the field with distance. Red curve: the NPM slab is inserted and the magnitude of the fields is evaluated once again at position 2. The resulting field magnitudes are more confined and show more detail than their counterparts without the lens, the green curves.

Fig. 6.
Fig. 6.

Intensity-map by a single molecule of the Ez field as a function of probe-sample distance. The molecule is DiIC18 and is excited with circularly polarized light of 514 nm (in vacuum). The NSOM probe has an aperture diameter of 130 nm. Below each image the respective distance is indicated, where a distance of zero nm equals the ‘in-contact’ situation. The fast decay of the field intensity with distance is evident, as well as the broadening of the pattern as is expected from the simulations.

Fig. 7.
Fig. 7.

Measured radial distribution of |Ez |2 as a function of distance. The origin maps to the center of the donut-shaped image in Fig. 6. Next to the measured data, a fit of the data with the Bethe-Bouwkamp model is also displayed (blue dots). Based on the fit, the theoretical curves for distances of 23 and 64 nm are calculated (orange and purple dots respectively). The broadening of the pattern with distance is apparent.

Fig. 8.
Fig. 8.

Measured FWHM of the |Ez |2 pattern in Fig. 7 as a function of distance. The measured data is obtained from Fig. 7 and the theoretical curve is obtained from the Bethe-Bouwkamp model. The model and the data are in good agreement, showing that the use of the FWHM of the Ez field as a quantitative means to investigate the influence of the negative permittivity material lens on image formation is very well feasible.

Equations (3)

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E ( x , y , z , t ) = k x , k y E ( k x , k y ) exp ( ik z z + ik x x + ik y y i ω t ) .
k z = ω 2 c 2 k x 2 k y 2 .
ε = ε ω p 2 ( ω 2 i ω γ ) .

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